Question

using euclids algorithm find hcf of 3141 and 1592​

Answer 1

Answer:

Euclid's Division Algorithm

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Euclid's division algorithm is a way to find the HCF of two numbers by using Euclid's division lemma. It states that if there are any two integers a and b, there exists q and r such that it satisfies the given condition a = bq + r where 0 ≤ r < b. Let's learn more about it in this lesson.

What is Euclid's Division Lemma?

Euclid’s Division Lemma (lemma is like a theorem) says that given two positive integers a and b, there exist unique integers q and r such that a = bq + r, 0≤ r <b. The integer q is the quotient and the integer r is the remainder. The quotient and the remainder are unique.

In simple words, Euclid's Division Lemma is what you were using to check the accuracy of division in lower classes, which is Dividend = Divisor × Quotient + Remainder. When we divide a=39 by b=5, we get the quotient as q=7 and the remainder as r=4. Here is an example:

Euclid's Division Lemma

Thus, by Euclid's division lemma, 39 = 5 × 7 + 4.

What is Euclid's Division Algorithm?

Euclid’s Division Algorithm is the process of applying Euclid’s Division Lemma in succession several times to obtain the HCF of any two

Answer 2

Answer:

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$3141 = 1592 \times 1 \times 1549 \\ 1592 = 1549 \times 1 + 43 \\ 1549 = 43 \times 36 + 1 \\ 43 = 1 \times 43 + 0 \\ \\ so \: hcf \: is \: 1$

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